Is this a feasible approach?
The project is feasible, given the right hardware. I don't think that using an LED as the detector is using the right hardware. There are light detecting resistors and other sensors that are more sensitive and faster reacting.
Would blink rate - sampling the analog input be a restriction.
Yes. But, if you can count the number of blinks in some period of time, so can the Arduino. If it's flashing too fast for you to count, it still may be glacial speed to the Arduino.
Recording when the on and off states are detected will let you distinguish between steady on, steady off, and blinking.